FIG. 1 illustrates a lens 12 transmitting light generated by a light source 10 such as a light emitting diode. A key issue in designing light sources to be used with optical systems comprised of passive optical imaging elements, such as lens 12, is illustrated in FIG. 1. Only light emitted from the source area that is consistent with the optical invariant or etendue of lens 12 can be usefully focused onto the target area 20 (for example, a transparent microdisplay). The etendue of a given optical system is defined as:E=∫∫(cos θ)dAdΩ  (1)where θ is the angle between the normal to the surface element dA and the centroid of the solid angle element dΩ. Etendue is a geometric property of the optics related to the divergence and cross-sectional area of the beam. The etendue cannot be decreased for if it were, the energy density at the image could exceed that of the source, violating the second law of thermodynamics.
Source 10 may be, for example, a light emitting diode (LED), which emits light in all directions. As illustrated in FIG. 1, only light 16 emitted from the center of the top surface of source 10 and within the cone accepted by the lens can be focused on the target 20. Light 14 emitted from the top of source 10 far from lens 12, and emitted near lens 12 but at an angle outside the etendue-limit, as well as light emitted from the sidewalls of source 10 (not shown), is not utilized by lens 12, and is lost. In the case of a light emitting diode light source 10, as the area of source 10 increases, in general the total light emitted from source 10 may also increase. However, the etendue of lens 12 imposes a maximum value on the amount of light flux that an optical system using lens 12 can utilize, regardless of how large light source 10 is made.
There are several ways to increase the amount of usefully captured light in an optical system. First, a lens with a larger diameter 20 may be used. However, as the diameter of a lens increases, the cost of the lens increases. Thus, it is desirable to limit the size of the lenses in an optical system, in order to control the cost.
Second, the light flux per unit area of the light source may be increased. In the case of a light emitting diode light source, the amount of light generated per unit area is generally proportional to the electrical current density in the light generating layers of the device. Thus, the light per unit area may be increased by increasing the current density. However, the efficiency of light emitting diodes usually falls at high current densities due to, for example, heating effects, saturation in the light emitting layers of the charge carriers that recombine to produce light, or the loss of confinement of the charge carriers that recombine to produce light. The loss of light generating efficiency at high current density limits the amount of light generated per unit area that can be created in a light emitting diode.